Quadratic Equation Solver
Solve ax² + bx + c = 0 — find the discriminant, both roots, the vertex, axis of symmetry, factorization, step-by-step solution, and a visual parabola plot. Handles real and complex roots.
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Applications
Quadratic equations appear throughout physics (projectile motion, harmonic oscillators), engineering (control systems, structural analysis), finance (profit maximization, break-even points), and computer graphics (Bézier curves, ray-quadric intersections).
The Formula
Solves ax² + bx + c = 0 using the Quadratic Formula: x = [−b ± √(b² − 4ac)] / 2a. The discriminant D = b² − 4ac determines the nature of the roots: D > 0 yields two distinct real roots, D = 0 yields one repeated real root, and D < 0 yields two complex-conjugate roots.
Fun Fact: The quadratic formula is over 4,000 years old — Babylonian clay tablets from around 2000 BC contain solved quadratic problems, long before the formal algebraic notation we use today.
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